Let Γ=(V,E) be a graph and ‎W_(‎a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),‎…‎ ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...

In this paper, we study the primitive ideals of quantum algebras supporting a rational torus action. We first prove a quantum analogue of a Theorem of Dixmier; namely, we show that the Gelfand-Kirillov dimension of primitive factors of various quantum algebras is always even. Next we give a combinatorial criterion for a prime ideal that is invariant under the torus action to be primitive. We us...

A cryptographic primitive or a security mechanism can be specified in a variety of ways, such as a condition involving a game against an attacker, construction of an ideal functionality, or a list of properties that must hold in the face of attack. While game conditions are widely used, an ideal functionality is appealing because a mechanism that is indistinguishable from an ideal functionality...

Trusted Network Connect (TNC) requires both user authentication and integrity validation of an endpoint before it connects to the internet or accesses some web service. However, as the user authentication and integrity validation are usually done via independent protocols, TNC is vulnerable to the Man-in-the-Middle (MitM) attack. This paper analyzes TNC which uses keys with Subject Key Attestat...

To any graph G can be associated a toric ideal I G. In this talk some recent joint work with Enrique Reyes and Christos Tatakis will be presented on the toric ideal of a graph. A characterization in graph theoretical terms of the elements of the Graver basis and the universal Gröbner basis of the toric ideal of a graph will be given. The Graver basis is the union of the primitive binomials of t...

The main aim of this paper is to investigate the structure of primitively generated connected braided bialgebras A with respect to the braided vector space P consisting of their primitive elements. When the Nichols algebra of P is obtained dividing out the tensor algebra T (P ) by the two-sided ideal generated by its primitive elements of degree at least two, we show that A can be recovered as ...

Curvature polynomials of cubic order are ideal primitive trajectories for car-like robots. Unlike the clothoids, which are linear curvature polynomials, cubic curves can be used to determine a unique trajectory to an arbitrary target posture using a single continuous primitive. Such curves are also the lowest order curves which are continuous in the torque applied to steering mechanisms, so the...

In this paper we give criteria for an ideal J of a TAF algebra A to be meet irreducible. We show that J is meet irreducible if and only if the C∗-envelope of A/J is primitive. In that case, A/J admits a faithful nest representation which extends to a ∗-representation of the C∗-envelope for A/J . We also characterize the meet irreducible ideals as the kernels of bounded nest representations; thi...